Solutions to exercises

Misprints

A list of corrections is available. Please
send me reports of misprints (an email link is given below).

A problem

Prove that there is no simple group of order 33.7.13.409.

Miscellany

1. Here is a picture of Muhammad Al-Khwarizmi, who
gave us the word "Algebra".

2. Can you explain what the following is about?

Curiously enough, the twelve-tone system has no zero in it.
Given a series: 3, 5, 2, 7, 10, 8, 11, 9, 1, 6, 4, 12 and the
plan of obtaining its inversion by numbers which when added
to the corresponding ones of the original series will give 12,
one obtains 9, 7, 10, 5, 2, 4, 1, 3, 11, 6, 8 and 12. For in
this system 12 plus 12 equals 12. There is not enough of zero
in it.

John Cage, "Eric Satie", in
Silence: Lectures and Writings, Calder and Boyars, 1968.

3. Hermann Weyl on Proposition 2.12(c), the statement that
(ST)-1=T-1S-1:

With this rule, although perhaps not with its mathematical expression,
you are all familiar. When you dress, it is not immaterial in which
order you perform the operations; and when in dressing you start with
the shirt and end up with the coat, then in undressing you observe the
opposite order; first take off the coat and the shirt comes last.

The mailing list
group-pub-forum
is for the discussion of any aspect of Group Theory. The reason for the name
is that the spirit is supposed to be
that of a conversation in a pub at a Group Theory conference.

GAP and MAGMA are systems for computation with algebraic structures
including groups and rings.